Abstract
We consider an infinite extension K of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. K is equipped with an inductive limit topology; its conjugate K; is a completion of K with respect to a topology given by certain explicitly written semi-norms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on K. If we deal with Galois extensions then all these objects are Galois-invariant.
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Kochubei, A.N. Analysis and Prbability over Infinite Extensions of a Local Field. Potential Analysis 10, 305–325 (1999). https://doi.org/10.1023/A:1008643901709
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DOI: https://doi.org/10.1023/A:1008643901709